We might very well discover that even Elo differences are not an absolute measure, but are relative to the pool of players that you use to determine the Elo. E.g. that when let two players of vast strength difference play in one pool of 1000 players, all playing enough games against each other so that statistical errors become completely insignificant, an you etermine an Elo from that.... That you get a very different resullt when you repeat that experiment with a ifferent group of 1000 players. In fact we alreay know this: if the pool of players are all versions of the same engine ('self play'), the Elo differences come out much larger than when you use unrelated engine opponents.

A zero Elo engine must lose every single game, assuming that it plays against an engine with 1 Elo or more (negative bias is also possible).

So, for instance, an engine that is actively trying to lose with incredible ability against an engine that is actively trying to win with incredible ability (consider SF playing loser's chess against SF playing normal chess) could possibly achieve 0 Elo.

But you have to be careful to avoid book lines that cause a draw. Also, the strong engine might force a draw because it does not know the opponent is trying to lose.

Taking ideas is not a vice, it is a virtue. We have another word for this. It is called learning.
But sharing ideas is an even greater virtue. We have another word for this. It is called teaching.

That's the obvious question to ask when reading something like the thread title, but when we looked at random movers a while back, it became apparent that they did not fit very well into the definition of "player", as assumed here:

The Elo rating system is a method for calculating the relative skill levels of players

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A "0 Elo player" may just make as little sense, after all, when someone is learning the rules of chess, he goes from a point where he breaks them too often, to be able to finish a legal game, to another where he actually can "play" a full game. By that time,they're far from 0, although they may still make the occasional illegal move (I've seen a federated player winning an official game by moving his rook to a different row and column in just one move, try getting that one past even a random mover).